- journal_title：Geophysics
- Contributor：Mark Pilkington
- Publisher：Society of Exploration Geophysicists
- Date：2009-
- Format：text/html
- Language：en
- Identifier：10.1190/1.3026538
- journal_abbrev：Geophysics
- issn：0016-8033
- volume：74
- issue：1
- firstpage：L7
- section：MAGNETIC EXPLORATION METHODS
I have developed an inversion approach that determines a 3D susceptibility distribution that produces a given magnetic anomaly. The subsurface model consists of a 3D, equally spaced array of dipoles. The inversion incorporates a model norm that enforces sparseness and depth weighting of the solution. Sparseness is imposed by using the Cauchy norm on model parameters. The inverse problem is posed in the data space, leading to a linear system of equations with dimensions based on the number of data, N. This contrasts with the standard least-squares solution, derived through operations within the M-dimensional model space (M being the number of model parameters). Hence, the data-space method combined with a conjugate gradient algorithm leads to computational efficiency by dealing with an 
system versus an 
one, where 
. Tests on synthetic data show that sparse inversion produces a much more focused solution compared with a standard model-space, least-squares inversion. The inversion of aeromagnetic data collected over a Precambrian Shield area again shows that including the sparseness constraint leads to a simpler and better resolved solution. The degree of improvement in model resolution for the sparse case is quantified using the resolution matrix.